Basic operations on Matrices

Aim: To generate matrix and perform basic operation on matrices Using MATLAB Software.

EQUIPMENTS:

  • PC with windows (Windows 7/8/10).
  • MATLAB Software

Theory:

%Creating a vector from a Known list of numbers:

A=input('enter the Matrix/Vector Elements')

enter the Matrix/Vector Elements 1 2 3 4

Result:

A  =   1    2    3   4

%Creating a vector with constant spacing by specifying the first term, spacing and the last term:

m=input('enter the first term')
q=input('enter the spacing')
%Default value of q is 1
n=input('enter the last term')
B=[m:q:n]

Result:

enter the first term m =2

enter the spacing q = 0.1000

enter the last term n =4

B  =

  column  1 to 12

   2.    2.1    2.2    2.3    2.4    2.5    2.6    2.7    2.8    2.9    3.    3.1  

  column 13 to 21

   3.2    3.3    3.4    3.5    3.6    3.7    3.8    3.9    4.  

%Creating a vector with constant spacing by specifying the first and the last terms, and the number of terms:

a=input('enter the first element')
b=input('enter the last element')
c=input('enter the number of elements')
C=linspace (a,b,c)

Result:

enter the first element a =3.

enter the last element b =6.

enter the number of elements c =5.

C = 3.    3.75    4.5    5.25    6

% Creating an All Zero Vector

m=input('enter the number of terms in the vector')
D=zeros(1,m)

Result:

enter the number of terms in the vector m =5.

D =0     0     0     0     0

% Creating a Vector consisting of all Ones

n=input('enter the number of terms in the vector')
E=ones(1,n)

Result:

enter the number of terms in the vector n =6.

E =1    1   1    1    1    1

% Measuring the size(number of elements) of the vector

A=[1 2 3 4]
l=length(A)

Result:

A =1     2     3     4

l = 4.

% Measuring the order of the vector

D= [1 1 1 1 1]
p=size (D)

Result:

D =1     1    1     1     1

p =1     5

disp('The number of rows is')
The number of rows is
disp(p(1))

   Result:   1.

disp('The number of columns is')
The number of columns is
disp(p(2))

    Result:   5.

% Transpose of a Matrix

A=[1 2 3 4]
A1=A'

Result:

A = 1.     2.     3.     4.

A1 =

    1.

    2.

    3.

    4.

% Multiplying each element of the vector/Matrix with a constant

k=input('enter the value of the Multiplying Constant')
B=[3 4 5 6]
B1=k*B

Result:

k =3.

B =3.     4.     5.     6.

B1 =9.    12.    15.    18.

%The above Multiplication operation can be done also as follows:

B11=k.*B

% Finding the sum of elements of a Matrix

A=[1  2.1 3.3  4]
S=sum(A)

Result:

A =1.    2.1    3.3    4.

S =10.4

B =
   1.    2.    3.  
   4.    5.    6.  
   7.    8.    9.  
S1=sum(B)

Result:

S1 = 45.  

%Finding the sum of each row and displaying in a column

S2=sum(B, 'c')

Result:

S2 =

     6.    

   15.  

   24.

% Finding the sum of each column and displaying in a row

S3=sum(B, 'r')

Result:

S3  =

       12.    15.    18.

% Finding the average of the elements of Matrix

B=[2  3  4  5]
Ave=mean(B)

Result:

B =2.     3.     4.     5.

Ave =3.5

%Finding the maximum and minimum values of a vector

A=[1  2 3 10.1 -1]
A1=max(A)
A2=min(A)  

Result:

A  =1.    2.    3.    10.1  - 1.  

A1  =10.1

A2= -1  

%Finding the product of the elements of a Matrix

A=[1  2  3  4]
P=prod(A)

Result:

A =1.     2.     3.     4.

P =24.

% Checking the sign of the elements of a Matrix

B=[-1 -2 3 4 -5 0]
S=sign(B)

% sign(B) returns 1 if the element of B is +ve, -1 if the element  is –ve and zero if the element is zero

Result:

B  =

  - 1.  - 2.    3.    4.  - 5.    0.  

S  =

 - 1.  - 1.    1.    1.  - 1.    0.  

% Finding the non zero elements of the Matrix

A=[-1  2  0  0  2  3]
S=find(A)

% find(A) returns the indices of the non- zero elements of A  

Result:

A = -1.     2.     0.     0.     2.     3.

S =1.     2.     5.     6.

% Arranging the elements of a Matrix in ascending/descending order

A=[1  23  45  6  73]
A1=sort(A,’ascend’)

Result:

A =1.    23.    45.     6.    73.

A1 =1.   6.    23.    45.    73.

% mtlb_sort(A) also will do the same

A2=sort(A, ’descend’)

Result:

A2= 73.    45.    23.     6.     1.

%Reshaping  the  Matrix

A=[1 2 3 4]
A1=matrix(A,4,1)
A2=A(:)
A3=matrix(A,2,2)

Result:

A =1.     2.     3.     4.

A1 =A2=

    1.

    2.

    3.

    4.

A3 =

    1.     3.

    2.     4.

% Extending the Dimension of the Matrix

A=[1 2 3]
%Appending a Row
A(2,:)=[4 5 6]

Result:

A =1.     2.     3.

A =1.     2.     3.

    4.     5.     6.

%%Appending a Column

A=[1 2 3]
A(:,4)= 10

Result:

A = 1.     2.     3.    10.      

%Deleting the elements of a Matrix

A=[1 2 3 4]
A =1.     2.   3.     4.
% Deleting the 4th column element
A(4)=[ ]

Result:

A =1.     2.    3.

%Arithmetic operations

%Addition of Two row matrices

A=[1 2 3]
B=[5 6 7]
S=A+B
D=A-B

Result:

A =1.     2.     3.

B =5.     6.     7.

S =6.     8.    10.

D = -4.    -4.    -4.

%Multiplication of Two Matrices

A=[1 2 3]
B=[2;3;4]
C=A*B  

Result:

A =1.     2.     3.

B =

    2.

    3.

    4.

C =20

% Element wise Multiplication

A=[1 2 3]
B=[3 4 5]
C=A.*B  

Result:

A =1.     2.     3.

B =3.     4.     5.

C =3.     8.    15.

%Element wise Division

A=[1 2 3]
B=[3 4 5]
C=A./B  

Result:

A =1.     2.     3.

B =4.     4.     6.

C =0.25    0.4    0.5

C1=A.\B

Result:

C1=3.    2.    1.6666667

%Raising each element of the matrix to 3rd power

A=[2  5 8]

B=A.^3

Result:

A =2.     5.     8.

B =8.   125.   512.

 

%Relational Operators

A=[1 2 3]
B=[5 3 1]
K=A>B
K1=A<B

Result:

A =1.     2.     3.

B =5.     3.     1.

K = F     F     T

K1=T    T     F

A=[1 2 3]
B=[1 3 3]
K=A<=B
K1=A>=B
K2=A==B

Result:

A =1.     2.     3.

B =1.     3.     3.

K = T    T     T

K1=T    F     T

K2=T    F     T

A=[1 2 3]
B=[1 3 3]
K=A~=B( not equal to)

Result:

A  =  1.    2.    3.  

B  =  1.    3.    3.  

K  =   F T F  

%Logical Operators

A=[1 2 3]
B=[2 0 4]
K=A|B
K1=A&amp;amp;amp;B

Result:

A =1.     2.     3.

B =2.     0.     4.

x =T     T     T

y =T     F     T

A=[1 0 3]
K=~A

Result:

A=1.     0.     3.

K =F    T     F

%These Programs explain  various (MxN) Matrix Operations:

%Creating a One-Dimensional Array/Vector:

A=input('enter the Matrix Elements')

Result:

enter the Matrix Elements[1 2 3;4 5 6;7 8 9]

A =

    1.     2.     3.

    4.     5.     6.

    7.     8.     9.

%creating a Matrix consisting of all zeros

A=zeros(3,2)

A =

    0.     0.

    0.     0.

    0.     0.

%creating a Matrix consisting of all Ones

B=ones(4,2)

Result:

B =

    1.     1.

    1.     1.

    1.     1.

    1.     1.

%Creating an Identity Matrix

A=eye(3,3)

Result:

A =

    1.    0.     0.

    0.    1.     0.

    0.    0.     1.

%Measuring the order of the vector

A=[1 2 3;4 5 6;2 3 -1]
p=size(A)

Result:

A =

    1.     2.     3.

    4.     5.     6.

    2.     3.    -1.

p=  3.     3.

disp('The number of rows is')

Result:

The number of rows is

disp(p(1))

   Result:

 3.

disp('The number of columns is')

Result:

The number of columns is

disp(p(2))

    Result:

3.

%Transpose of a Matrix

A=[1 2 3 ;10 11 12; 34 45 89]
A1=A'

 Result:

A =

    1.     2.     3.

   10.    11.    12.

   34.    45.    89.

A1 =

    1.    10.    34.

    2.    11.    45.

    3.    12.    89.

%Multiplying each element of the Matrix with a constant

k=input('enter the value of the Multiplying Constant')
B=[3 4 5 6;2 4 6 8]
B1=k*B

Result:

enter the value of the Multiplying Constant

k =4

B =

    3.     4.     5.     6.

    2.     4.     6.     8.

B1 =

   12.    16.    20.    24.

    8.    16.    24.    32.

%The above Multiplication operation can be done also as follows:

B11=k.*B

%Finding the sum of element of a Matrix

A=[1  2 ;3 4;5 6]
S=sum(A)

Result:

A =

    1.     2.

    3.     4.

    5.     6.

S =21.

%Finding the average of the elements of Matrix

B=[2 3 4;4 5 6]
Ave=mean(B)

Result:

B =

    2.     3.     4.

    4.     5.     6.

Ave =

    4.

%Finding the maximum and minimum values of a vector

A=[1 2 3; 10  2  -1]
A1=max(A)
A2=min(A)  
P=prod(A)

Result:

A =

    1.     2.     3.

   10.     2.    -1.

A1 =10.

A2 = -1.

P = -120.  

%Checking the sign of the elements of a Matrix

B=[-1 -2 3;4 -5 0]
S=sign(B)
%sign(B) returns 1 if the element of B is +ve, -1 if the element  is –ve and zero if the element is zero

Result:

B =

   -1.    -2.     3.

    4.    -5.     0.

S =

   -1.    -1.     1.

    1.    -1.     0.

%Finding the non zero elements of the Matrix

A=[-1 2 0; 0 2 3]
S=find(A)
%find(A) returns the indices of the non- zero elements of A  

Result:

A =

   -1.     2.     0.

    0.     2.     3.

S = 1.    3.    4.    6.

% checking a matrix whether is empty or not

A=[1 2 3 0]
K= isempty(A)
%isempty() returns a true value for an empty matrix

Result:

A  =

     1.    2.    3.    0.  

K  = F  

%Arranging the elements of a Matrix in ascending/descending order

A=[1 23 45; 6 7 3]
A1=sort(A,’descend’)
%each column of A is sorted

Result:

A =

    1.    23.    45.

    6.     7.     3.

A1 =

   6.    23.    45.  

   1.    7.     3.

A1=sort(A, ‘ascend’)
%each row of A is sorted

Result:

A1=

   45.    23.    1.  

   7.     6.     3.  

%all the elements  of A are sorted in increasing order

A1  =

   1.    6.    23.  

   3.    7.    45.

% all the elements  of A are sorted in decreasing  order

A1=sort(A, ‘desccend’)

A1  =

   45.    7.    3.  

   23.    6.    1.

%Reshaping  the  Matrix

A=[1 2 3 4;3 5 6 7]
A1=matrix(A,4,2)
A2=matrix(A,1,8)

Result:

A =

    1.     2.     3.     4.

    3.     5.     6.     7.

A1 =

    1.     3.

    3.     6.

    2.     4.

    5.     7.

A2 =

    1.     3.     2.     5.     3.     6.     4.     7.

%Extending the Dimension of the Matrix

A=[1 2 3;4 5 6]

%Appending a Row

A(3,:)=[10 15 26]

Result:

A=    1.    2.    3.  

        4.    5.    6.  

A  =

    1.     2.     3.    

    4.     5.     6.    

   10.    15.    26.

%Appending a Column

A(:,4)=[10;20;87]

A= 1.     2.     3.     10.

    4.     5.     6.     20.

   10.   15.   26.    87.

 

%Appending an Intermediate  row  

A=[1 2 3;4 5 6;7 8 9]

A =

    1.     2.     3.

    4.     5.     6.

    7.     8.     9.

%Appending a  row between 1st and 2nd rows

A=[A(1,:); 10 11 12;A(2,:);A(3,:)]

Result:

A =

    1.     2.     3.

   10.    11.    12.

    4.     5.     6.

    7.     8.     9.

%Appending a column between 2nd and 3rd column

A=[1 2 3;4 5 6;7 8 9]
A=[A(:,1) A(:,2) [10;12;15;16] A(:,3)]

Result:

A =

    1.     2.    10.     3.

   10.    11.  12.    12.

    4.     5.    15.     6.

    7.     8.    16.     9.      

%Deleting the row/column of a Matrix

A=[1 2 3; 4 5 6]
%Deleting the 2nd  row  
A(2,:)=[ ]

Result:

A =

    1.     2.     3.

    4.     5.     6.

A =

    1.     2.     3.

%Deleting the 2nd column

A=[1 2 3; 4 5 6]
A(:,2)=[ ]

Result:

A =

    1.     2.     3.

    4.     5.     6.

A =

       .   3.

    4.     6.

 

%Arithmetic operations

%Addition of Two row matrices

A=[1 2 3;4 5 6]
B=[5 6 7;10 11 12]
S=A+B
D=A-B

Result:

A =

    1.     2.     3.

    4.     5.     6.

B =

    5.     6.     7.

   10.    11.    12.

S =

    6.     8.    10.

   14.    16.    18.

D =

   -4.    -4.    -4.

   -6.    -6.    -6.

%Multiplication of Two Matrices

A=[1 2 3;4 5 6]
B=[5 6 3;10 11 12;3 4 6]
C=A*B

Result:

A =

    1.     2.     3.

    4.     5.     6.  

B =

    5.     6.     3.

   10.    11.    12.

    3.     4.     6.

C =

   34.    40.    45.

   88.   103.   108.  

%Element wise Multiplication

A=[1 2 3;4 5 6]
B=[3 4 5;3 2 1]
C=A.*B  

Result:

A =

    1.     2.     3.

    4.     5.     6.

B =

    3.     4.     5.

    3.     2.     1.

C =

    3.     8.    15.

   12.    10.     6.

%Element wise Division
C=A./B  

Result:

C =

   0.3333    0.5000    0.6000

   1.3333    2.5000    6.0000

%Raising each element of the matrix to 4th  power

A=[2 5 8;4 5 6]
B=A.^4

Result:

A =

    2.     5.     8.

    4.     5.     6.

B =

         16.         625.        4096.

        256.        625.       1296.

 

%Relational Operators

A=[1 2 3;10 3 5]
B=[5 3 1;0 3 6]
K=A>B
x=A<B
y=A<=B
K1=A>=B
K2=A==B
K3=A~=B

Result:

A =

    1.     2.     3.

   10.     3.     5.

B =

    5.     3.     1.

    0.     3.     6.

K =

    F     F     T

    T     F     F

x =

    T     T     F

    F     F     T

y =

    T     T     F

    F     T     T

K1 =

    F     F     T

    T     T     F

K2 =

    F     F     F

    F     T     F

K3 =

    T      T     T  

    T      F     T  

%Logical Operators

A=[1 2 3;0 0 1;1 -1 0]
B=[2 0 4;-1 2 -3;9 8 0]
K=A|B
K1=A&amp;amp;B

Result:

A =

    1.     2.     3.

    0.     0.     1.

    1.    -1.     0.

B =

    2.     0.     4.

   -1.     2.    -3.

    9.     8.     0.

K =

    T   T   T  

    T   T   T  

    T   T   F  

K1 =

    T   F   T  

    F   F   T  

    T   T   F

A=[1 0 3;2 -1 0;3 2 -1]
K=~A/k=not(A)

Result:

A =

    1     0     3

    2    -1     0

    3     2    -1

K =

    F   T   F  

    F   F   T  

Viva Questions:

1. What is the command to generate row matrix?

R=[a,b,c]

2. What is the command to generate column matrix?

colvec = [a ; b ; c]

3. What is the command to generate matrix?

matrix=[1,2,3;4,5,6;7,8,9]

4. What is the command to find Inverse matrix?

Inverse_matrix= Inv(m).

  • Created
    Oct 15, 2019
  • Updated
    Feb 12, 2020
  • Views
    211